The role of parameter Jacobians in the stability of network outputs

What the math gives to ML

The paper provides a concrete criterion for judging whether parameter-direction pruning preserves task-relevant network behavior: the discarded part of the parameter Jacobian must capture only a small fraction of every task-relevant tangent vector. This is more informative than weight magnitude because it measures how parameter removal changes output-space dynamics, and it naturally connects pruning to fixed-kernel NTK evolution. A practical transfer is a calibration-time Jacobian-aware pruning method that selects a mask subject to an empirical tangent-capture constraint, then tests whether the pruned model preserves loss trajectories and fine-tuning stability at substantially lower parameter and inference cost. The available extraction does not expose the complete finite-time semigroup bound, so the implementable proposal below uses the explicit tangent inequality as a pruning certificate rather than claiming an unavailable numerical constant.